In
astronomical navigation
Celestial navigation, also known as astronavigation, is the practice of position fixing using stars and other celestial bodies that enables a navigator to accurately determine their actual current physical position in space (or on the surface of ...
, the intercept method, also known as Marcq St. Hilaire method, is a method of calculating an observer's position on earth (
geopositioning
Geopositioning, also known as geotracking, geolocalization, geolocating, geolocation, or geoposition fixing, is the process of determining or estimating the geographic position of an object.
Geopositioning yields a set of geographic coordinates ...
). It was originally called the ''azimuth intercept'' method because the process involves drawing a line which intercepts the
azimuth
An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north.
Mathematicall ...
line. This name was shortened to ''intercept'' method and the ''intercept distance'' was shortened to 'intercept'.
The method yields a
line of position
A position line or line of position (LOP) is a line (or, on the surface of the earth, a curve) that can be both identified on a chart (nautical chart or aeronautical chart) and translated to the surface of the earth. The intersection of a minimum o ...
(LOP) on which the observer is situated. The intersection of two or more such lines will define the observer's position, called a "fix". Sights may be taken at short intervals, usually during hours of twilight, or they may be taken at an interval of an hour or more (as in observing the Sun during the day). In either case, the lines of position, if taken at different times, must be advanced or retired to correct for the movement of the ship during the interval between observations. If observations are taken at short intervals, a few minutes at most, the corrected lines of position by convention yield a "fix". If the lines of position must be advanced or retired by an hour or more, convention dictates that the result is referred to as a "running fix".
Summary
The intercept method is based on the following principle.
The actual distance from the observer to the geographical position (GP) of a celestial body (that is, the point where it is directly overhead) is "measured" using a
sextant
A sextant is a doubly reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of celes ...
. The observer has already estimated his position by
dead reckoning
In navigation, dead reckoning is the process of calculating current position of some moving object by using a previously determined position, or fix, and then incorporating estimates of speed, heading direction, and course over elapsed time. ...
and calculated the distance from the estimated position to the body's GP; the difference between the "measured" and calculated distances is called the intercept.
The diagram on the right shows why the zenith distance of a celestial body is equal to the angular distance of its GP from the observer's position.
The rays of light from a celestial body are assumed to be parallel (unless the observer is looking at the moon, which is too close for such a simplification). The angle at the centre of the Earth that the ray of light passing through the body's GP makes with the line running from the observer's
zenith
The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" ...
is the same as the zenith distance. This is because they are
corresponding angles
In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing whether two or more other lines in the Euclidean plane are parallel. The intersections of a ...
. In practice it is not necessary to use zenith distances, which are 90° minus altitude, as the calculations can be done using observed altitude and calculated altitude.
Taking a sight using the intercept method consists of the following process:
* Observe the altitude above the horizon Ho of a celestial body and note the time of the observation.
* Assume a certain geographical position (lat., lon.), it does not matter which one so long as it is within, say, 50 NM of the actual position (or even 100 NM would not introduce too much error). Compute the altitude Hc and azimuth Zn with which an observer situated at that assumed position would observe the body.
* If the actual observed altitude Ho is smaller than the computed altitude Hc this means the observer is farther away from the body than the observer at the assumed position, and vice versa. For each minute of arc the distance is one NM and the difference between Hc and Ho expressed in minutes of arc (which equal NM) is termed the "intercept". The navigator now has computed the intercept and azimuth of the body.
* On the chart he marks the assumed position AP and draws a line in the direction of the azimuth Zn. He then measures the intercept distance along this azimuth line, towards the body if Ho>Hc and away from it if Ho
Methodology
Suitable bodies for celestial sights are selected, often using a Rude Star Finder. Using a sextant
A sextant is a doubly reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of celes ...
, an altitude is obtained of the sun, the moon, a star or a planet. The name of the body and the precise time of the sight in UTC is recorded. Then the sextant is read and the altitude (''Hs'') of the body is recorded. Once all sights are taken and recorded, the navigator is ready to start the process of sight reduction In astronavigation, sight reduction is the process of deriving from a sight, (in celestial navigation usually obtained using a sextant), the information needed for establishing a line of position, generally by intercept method.
Sight is defined ...
and plotting.
The first step in sight reduction is to correct the sextant altitude for various errors and corrections. The instrument may have an error, IC or index correction (See article on adjusting a sextant). Refraction by the atmosphere is corrected for with the aid of a table or calculation and the observer's height of eye above sea level results in a "dip" correction, (as the observer's eye is raised the horizon dips below the horizontal). If the Sun or Moon was observed, a semidiameter correction is also applied to find the centre of the object. The resulting value is "observed altitude" (''Ho'').
Next, using an accurate clock, the observed celestial object's geographic position (''GP'') is looked up in an almanac. That's the point on the Earth's surface directly below it (where the object is in the zenith
The zenith (, ) is an imaginary point directly "above" a particular location, on the celestial sphere. "Above" means in the vertical direction (plumb line) opposite to the gravity direction at that location (nadir). The zenith is the "highest" ...
). The latitude of the geographic position is called declination, and the longitude is usually called the hour angle
In astronomy and celestial navigation, the hour angle is the angle between two planes: one containing Earth's axis and the zenith (the '' meridian plane''), and the other containing Earth's axis and a given point of interest (the ''hour circle'' ...
.
Next, the altitude and azimuth of the celestial body are computed for a selected position (assumed position or AP). This involves resolving a spherical triangle. Given the three magnitudes: local hour angle (''LHA''), observed body's declination (''dec''), and assumed latitude (''lat''), the altitude ''Hc'' and azimuth ''Zn'' must be computed. The local hour angle, ''LHA'', is the difference between the AP longitude
Longitude (, ) is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter l ...
and the hour angle of the observed object. It is always measured in a westerly direction from the assumed position.
The relevant formulas (derived using the spherical trigonometric identities) are:
:
:
:The adjustment from Z to Zn (which is in